Powers of tight Hamilton cycles in randomly perturbed hypergraphs

Wiebke Bedenknecht; Jie Han; Yoshiharu Kohayakawa; Guilherme O. Mota

doi:10.1002/rsa.20885

Powers of tight Hamilton cycles in randomly perturbed hypergraphs

Wiebke Bedenknecht
, Jie Han^*
, Yoshiharu Kohayakawa
, Guilherme O. Mota

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

26 Citations (Scopus)

Abstract

For k ≥ 2 and r ≥ 1 such that k + r ≥ 4, we prove that, for any α > 0, there exists ε > 0 such that the union of an n-vertex k-graph with minimum codegree (Formula presented.) and a binomial random k-graph (Formula presented.) with (Formula presented.) on the same vertex set contains the rth power of a tight Hamilton cycle with high probability. This result for r = 1 was first proved by McDowell and Mycroft.

Original language	English
Pages (from-to)	795-807
Number of pages	13
Journal	Random Structures and Algorithms
Volume	55
Issue number	4
DOIs	https://doi.org/10.1002/rsa.20885
Publication status	Published - 1 Dec 2019
Externally published	Yes

Keywords

perturbed hypergraphs
powers of Hamilton cycles
random hypergraphs

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10.1002/rsa.20885

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title = "Powers of tight Hamilton cycles in randomly perturbed hypergraphs",

abstract = "For k ≥ 2 and r ≥ 1 such that k + r ≥ 4, we prove that, for any α > 0, there exists ε > 0 such that the union of an n-vertex k-graph with minimum codegree (Formula presented.) and a binomial random k-graph (Formula presented.) with (Formula presented.) on the same vertex set contains the rth power of a tight Hamilton cycle with high probability. This result for r = 1 was first proved by McDowell and Mycroft.",

keywords = "perturbed hypergraphs, powers of Hamilton cycles, random hypergraphs",

author = "Wiebke Bedenknecht and Jie Han and Yoshiharu Kohayakawa and Mota, \{Guilherme O.\}",

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AU - Bedenknecht, Wiebke

AU - Han, Jie

AU - Kohayakawa, Yoshiharu

AU - Mota, Guilherme O.

PY - 2019/12/1

Y1 - 2019/12/1

N2 - For k ≥ 2 and r ≥ 1 such that k + r ≥ 4, we prove that, for any α > 0, there exists ε > 0 such that the union of an n-vertex k-graph with minimum codegree (Formula presented.) and a binomial random k-graph (Formula presented.) with (Formula presented.) on the same vertex set contains the rth power of a tight Hamilton cycle with high probability. This result for r = 1 was first proved by McDowell and Mycroft.

AB - For k ≥ 2 and r ≥ 1 such that k + r ≥ 4, we prove that, for any α > 0, there exists ε > 0 such that the union of an n-vertex k-graph with minimum codegree (Formula presented.) and a binomial random k-graph (Formula presented.) with (Formula presented.) on the same vertex set contains the rth power of a tight Hamilton cycle with high probability. This result for r = 1 was first proved by McDowell and Mycroft.

KW - perturbed hypergraphs

KW - powers of Hamilton cycles

KW - random hypergraphs

UR - https://www.scopus.com/pages/publications/85070254731

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DO - 10.1002/rsa.20885

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IS - 4

ER -

Powers of tight Hamilton cycles in randomly perturbed hypergraphs

Abstract

Keywords

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